Bond

What is the different between add-on and discount in calculation?

Example:

The following are 90-day money market instruments:

Instrument A=Quote: 5.78%, 360 days, discount rate

Instrument B=Quote: 5.96%, 365 days, add-on rate

Which has the highest rate of return?

What we are required to do basically is to convert either one of them to be of the same quotation as the other i.e. Convert Instrument A from Bank Discount Yield (“BDY”) to Add-On Rate (“AOR”) or vice-versa for Instrument B. In my working below, I will convert BDY of A to AOR.

The formula for BDY is = [ (P1-Po)/ P1 ] * (360/t)  where P1 is the par value of the instrument, Po is the current value of the instrument and t is the duration of the instrument

We are given that BDY is 5.78% and we know P1 (we can assign a arbitary value of 100 or 1,000 ) and we need to solve for Po.

Equating the above equation to 5.78% we obtain a value of 98.555 for Po.

Next we will determine the AOR for Instrument A. We know that Instrument B is quoted as AOR on a 365 days basis. This basically means:

                                        AOR= [ (P1-Po)/ Po ] * (365/t)

*Note that now the denominator is Po instead of P1*

AOR can be quoted on either a 360 days or 365 days basis.

If you now plug the values into the AOR formula you will get: 5.9462% ( < 5.96%)